\begin{table}[!t]
\centering  
\caption{\label{TestResultsTradeWar} 
 Testing Predictions about the Welfare Impact of the US-China Trade War}  
\begin{tabular}{lccccc}\toprule

Goodness-of-fit measure: & Correlation   && \multicolumn{3}{c}{IV-Based Test} \\  \cline{2-2}  \cline{4-6}
& 			  && $\qquad$ Naive IV $\qquad$ && Preferred IV     \\ 
& $Corr \left(\Delta y_n, \Delta x_n (\hat{\theta}) \right)$ && $\hat{\beta}_{z^{\text{naive}}} (\hat{\theta})$ && $\hat{\beta}_{z^{\text{pref}}} (\hat{\theta}) $ \\ 
& (1) && (2) && (3) \\ \hline


Point estimate	&	0.04	&&	0.59	&&	0.15	\\ [8pt]						
\multicolumn{6}{l}{Inference ignoring estimation uncertainty}\\							 $\quad$ Std. error 	&		&&	0.66	&&	0.21	\\ $\quad$ p-value of H0: $\hat{\beta}=0$	&		&&	0.36	&&	0.48	\\ [8pt]

\multicolumn{6}{l}{Inference accounting for estimation uncertainty}\\							 $\quad$ Std. error 	&		&&	0.67	&&	0.23	\\ $\quad$ p-value of H0: $\hat{\beta}=0$	&		&&	0.37	&&	0.52	\\ 



 \bottomrule
\end{tabular}\\
\vspace{-0.3cm}
\justify \footnotesize \emph{Notes:} All statistics are based on the pooled sample of changes in 24,193 welfare-relevant outcomes, and FGKK's estimates $\hat{\theta}$, as described in Section \ref{subsec:Simulation-Procedure}. Column (1) reports the correlation between actual changes and the predicted impact of the US-China trade war across all outcomes. Columns (2) and (3) implement our IV-based test using the naive IV $z^{\text{naive}}$, as defined by equations (\ref{eq:naive}) and (\ref{eq:tariff_shifter_application}), and our preferred IV $z^{\text{pref}}$, as defined by equations (\ref{eq:preferred}) and (\ref{eq:tariff_shifter_application}). Inference ignoring estimation uncertainty is as described in Section \ref{subsec:IVTest}. Inference accounting for estimation uncertainty is as described in Appendix \ref{subsec:Implementation}.
\end{table}